Quantifying the age structure of free‐ranging delphinid populations: Testing the accuracy of Unoccupied Aerial System photogrammetry

Abstract Understanding the population health status of long‐lived and slow‐reproducing species is critical for their management. However, it can take decades with traditional monitoring techniques to detect population‐level changes in demographic parameters. Early detection of the effects of environmental and anthropogenic stressors on vital rates would aid in forecasting changes in population dynamics and therefore inform management efforts. Changes in vital rates strongly correlate with deviations in population growth, highlighting the need for novel approaches that can provide early warning signs of population decline (e.g., changes in age structure). We tested a novel and frequentist approach, using Unoccupied Aerial System (UAS) photogrammetry, to assess the population age structure of small delphinids. First, we measured the precision and accuracy of UAS photogrammetry in estimating total body length (TL) of trained bottlenose dolphins (Tursiops truncatus). Using a log‐transformed linear model, we estimated TL using the blowhole to dorsal fin distance (BHDF) for surfacing animals. To test the performance of UAS photogrammetry to age‐classify individuals, we then used length measurements from a 35‐year dataset from a free‐ranging bottlenose dolphin community to simulate UAS estimates of BHDF and TL. We tested five age classifiers and determined where young individuals (<10 years) were assigned when misclassified. Finally, we tested whether UAS‐simulated BHDF only or the associated TL estimates provided better classifications. TL of surfacing dolphins was overestimated by 3.3% ±3.1% based on UAS‐estimated BHDF. Our age classifiers performed best in predicting age‐class when using broader and fewer (two and three) age‐class bins with ~80% and ~72% assignment performance, respectively. Overall, 72.5%–93% of the individuals were correctly classified within 2 years of their actual age‐class bin. Similar classification performances were obtained using both proxies. UAS photogrammetry is a non‐invasive, inexpensive, and effective method to estimate TL and age‐class of free‐swimming dolphins. UAS photogrammetry can facilitate the detection of early signs of population changes, which can provide important insights for timely management decisions.


| INTRODUC TI ON
The ability to monitor the health status and dynamics and detect trends of free-ranging populations is critical for the effective management of long-lived and slow-reproducing species (Holmes & York, 2003;Jackson et al., 2020). For marine mammals, anthropogenic and environmental stressors can affect individual health and vital rates (e.g., fertility and survival; Pirotta et al., 2019) and subsequently cause population-level impacts (e.g., habitat shift, and abundance decline; Pirotta et al., 2015;Senigaglia et al., 2016). A decline in population abundance and/or changes in vital rates can provide an early warning for the sustainability of a population. Therefore, early detection of stressor effects on individuals could help forecast potential impacts at the population level.
Consequently, these traditional techniques often have a limited statistical power to estimate a population trend or detect a change in the trend . Thus, relying only on abundance estimation to monitor population dynamics can inhibit timely conservation and management actions (Taylor & Gerrodette, 1993;Thompson et al., 2000;Turvey et al., 2007). Furthermore, the typical frequency of surveys and imprecision of abundance estimates may fail to detect precipitous declines in abundance , highlighting the need for alternative techniques to help detect early warning signs of population declines.
Population dynamics are a function of key parameters, such as population growth and age structure (Clark et al., 2000;Jackson et al., 2020), which are function of vital rates (Ozgul et al., 2010) and environmental factors (e.g., Pardo et al., 2013;Weimerskirch, 2018). A stable age distribution is an indicator of population health, that is, the population contains a fixed proportion of newborn, immature, and mature individuals (Gamelon et al., 2016), while deviances from this distribution would lead to either population growth or decline (Coulson et al., 2005;Jackson et al., 2020;Jones et al., 2018). Therefore, detecting changes in the age structure of a population may provide an early sign of future changes in abundance (Booth et al., 2020;Holmes & York, 2003;Reichert et al., 2016). Few studies have focused on estimating the age structure of cetaceans to monitor population health (Evans & Hindell, 2004;Guo et al., 2020;Pallin et al., 2022).
Non-invasive technologies such as aerial photogrammetry using Unoccupied Aerial Systems (UASs or "drones") have become common practice in baleen whale health monitoring studies Christiansen et al., 2018Christiansen et al., , 2022Dawson et al., 2017). To date, few studies have examined the performance of UAS photogrammetry to monitor the health of toothed whales (Cheney et al., 2022;Currie et al., 2021;Fearnbach et al., 2018). UAS photogrammetry allows for large groups of animals to be sampled with minimal effort (Booth et al., 2020), suggesting that UAS photogrammetry might be a suitable and costeffective tool to monitor changes in the age structure of delphinid populations.
The overall aim of this study was to use UAS photogrammetry to develop a length-based method of estimating the age-class of free-ranging delphinids. First, we evaluated the precision (variation between measurements) and accuracy (consistency between the estimated and observed measurements) of UAS photogrammetry for measuring and estimating the total body length (TL) of bottlenose dolphins (Tursiops truncatus) under human care. Second, we tested whether individual bottlenose dolphins could be assigned to correct age-classes from simulated UAS photogrammetry length estimates as a means of quantifying the age structure of a well-studied, freeranging dolphin community. Findings are discussed in the context of providing rapid and important insights for timely management and conservation of cetacean populations.

| Facilities, study animals, and length measurements
We physically measured TL (i.e., the tip of the rostrum to the tip of the natural notch created by the overlapping fluke lobes ( Figure A1), hereafter referred to as the notch) and blowhole to dorsal fin (BHDF) for 18 bottlenose dolphins under human care at two facilities in Hawaiʻi, USA (Figure 1a). The distance from the center of the blowhole to the anterior insertion of the dorsal fin is an established proxy for TL in bottlenose dolphins van Aswegen et al., 2019). Six adult males ranging from 11.5 to 34.5 years of age (mean = 23.6 ± 7.9 years) four individuals (two males and two females) were born in the Gulf of Mexico. The age of these animals was based on the size that they were when collected. Dolphins were measured in a stationary and straight position for all measurements. TL was collected on the ventral side of the dolphin in an inverted position using a tape measure attached to a rigid PVC pipe. The base of the measuring pipe was placed onto a rigid plate aligned with the tip of the rostrum to allow for straight-line measurements. BHDF measurements were made from the center of the blowhole to the insertion of the dorsal fin using a soft measuring tape. One measurement set (consisting of two to three replicates per measurement) was collected on the day or within a week of the UAS sampling (see below). To increase sample size, four to six additional replicates were collected within the next 7 months (total of 7-10 TL and BHDF measurements per animal). DQH measurements per animal were collected on the same day.

| Length measurements via UAS photogrammetry
Aerial imagery of the six dolphins at DQO was collected by two UAS platforms during June 2019. However, individual A was sampled by one platform only due to weather (Table A2) (Dawson et al., 2017) was attached to both platforms, providing an accuracy of 0.1 m and resolution of 1 cm. Despite the precision, some inaccurate altitude readings were recorded. To correct these errors, a custom-made smoother was applied to the original data. The Inspire-2 recorded videos in 4 k resolution (3840 × 2150 pixels), while photographs (4608 × 3456 pixels) were taken with the APH-22. Consecutive flights using both platforms (n = 24 flights in total) were conducted at five altitudes (16, 20, 30, 40, and 50 m).   Table A1.
photographs were selected when both the blowhole and dorsal fin insertion were visible and when the individual's body was as straight and horizontal as possible (i.e., minimal body arch). Available images of sufficient quality varied by platform (Table A2). In total, 144 video stills (75 stationary and 69 surfacing) from the Inspire-2 and 127 photographs (65 stationary and 62 surfacing) of sufficient quality were used to compare the platforms (Table A2). Due to weather or the lack of images of sufficient quality, individual A (APH-22) and individual F were removed from the analyses (both platforms).
Images from each platform were processed by two independent observers using an updated version of the Graphical User Interface (GUI) described in Dawson et al. (2017). Image processing consisted of measuring TL and BHDF for stationary animals and measuring BHDF for surfacing animals. Using a Wilcoxon test, no significant differences in accuracy (Table A4) were found between observers for the measurements made for each platform (Table A3). However, there were significant differences between observers across platforms (Table A4), with the APH-22 observers producing more precise measurements of TL and more accurate measurements of BHDF (Table A3). The sample of APH-22 images was smaller than that of the Inspire-2 because suitable images were more likely to be obtained from the Inspire-2 video footage than the APH-22 photographs (Table A2). Given the inter-observer reliability and greater efficiency of the Inspire-2, only Observer 1's measurements of the Inspire-2 video-still images were used for the remainder of the study.

| Calculating the error of UAS measurements
Using a frequentist approach, UAS photogrammetry error was calculated as the difference between the physical and UAS measurements of TL and BHDF from five stationary animals at DQO. We quantified the relationship between physical measurements of TL (cm) and BHDF (cm, a proxy for TL) of the 18 Dolphin Quest animals ( Figure A2) and tested three models (ratio of BHDF/TL, linear, logtransformed linear) to estimate TL via BHDF (see Methods A1). To first evaluate the performance of these models (Methods A1), each model's coefficients were used to separately estimate TL based on physical measurements of BHDF (BHDF Physical ) from the five stationary dolphins at DQO. Since the models performed well on physical measurements (Table 2), we then used them to estimate TL from UAS-measured BHDF (BHDF UAS ) for five surfacing animals (see Methods A1). The error (± standard deviation, SD) in estimating TL from BHDF for the surfacing animals was calculated for each model (see Methods A2). Based on the model performances (Table 2), the log-transformed linear model was considered the best model for use in subsequent analyses. Table 1 summarizes the data sources, data types, and associated analyses for this and the following section.

| Testing the performance of UAS estimates to infer age-class
To test the feasibility of assigning individuals to age-class bins using UAS estimates of TL (from BHDF), we employed a long-term morphometric dataset of bottlenose dolphins from the SDRP.
Since 1984, the SDRP has been conducting periodic catch-andrelease of individuals for life history studies and health assessment (Wells, 2009;Wells et al., 2004). During these assessments, physical measurements of dolphins were obtained, including TL and other measurements we used to derive BHDF ( Figure 1b). In total, 742 health assessments were made of 263 unique individuals of both sexes during 1984-2019. We used the following information from the SDRP dataset: age (years, either empirical DOB from observations of the animal and its identifiable mother, or, if the DOB was unknown, an estimate from growth layer groups in a tooth extracted under local anesthesia (Hohn et al., 1989)); TL (cm), distance between the tip of the rostrum and the center of the caudal edge of the blowhole (cm); and distance between the tip of the rostrum and the anterior insertion of the dorsal fin (cm). BHDF for each animal in the SDRP dataset was calculated by subtracting the second-to-last measurement from the last. While these BHDF measurements include the diameter of the blowhole, we assumed they did not differ significantly from BHDF measurements that terminate in the center of the blowhole (difference of approximately 1 cm, F.V. personal observation).
F I G U R E 2 UAS video-still images of an individual bottlenose dolphin at Dolphin Quest Oʻahu (HI, USA). UAS measurements were collected for (a) stationary and (b) surfacing animals while swimming. UAS measurements consisted of the TL (i.e., tip of the rostrum to the notch in the flukes; dashed blue line shown in (a), and BHDF (i.e., the center of the blowhole to the anterior insertion of the dorsal fin; orange arrows shown in (a) and (b)). BHDF, blowhole to dorsal fin distance; TL, total length; UAS, Unoccupied Aerial System.
We followed a frequentist approach to test the performance of UAS photogrammetry in inferring age-class. New sets of BHDF measurements and associated TL estimates were simulated for the SDRP long-term morphometric dataset by applying the UAS errors (±SD) in estimating TL using BHDF of surfacing animals. However, because of the limited sample size (n = 5) and overall above-average TL/BHDF relationship resulting from the physical measurements of the DQO individuals compared with the DQH individuals ( Figure A2), the error of the UAS-simulated measurements was set to 0 plus the calculated SD. This prevented from overestimating the size of the SDRP dolphins. First, the UAS-simulated measurements of BHDF were calculated following: where BHDF UAS_sim is the UAS-simulated BHDF measurement, BHDF SDRP_physical is the physical measurement of BHDF (from the SDRP dataset), N is the normal distribution, n is the number of SDRP individuals, D e_BHDF is the UAS error calculated with BHDF of surfacing animals, and D sd_BHDF is the UAS SD for the UAS-measurement error.
Similarly, UAS-simulated TL estimates based on BHDF UAS_sim were calculated: where TL UAS_sim is the UAS-simulated TL, TL Est.log.linear is the TL estimated by the log-transformed linear model (Equation S4) using BHDF UAS_sim , N is the normal distribution, n is the number of SDRP individuals, D e is the UAS error with estimates of TL via BHDF of surfacing animals, and D sd is the SD for the UAS-measurement error.

| Calculating the error between physical versus UAS measurements
The average difference between the TL measurements of stationary dolphins by physical and UAS methods was 0.1 ± 1.3% (mean ± SE) across all five altitudes ( Figure 3). The levels of accuracy of UAS measurements were similar regardless of altitude, suggesting that sampling can be successfully conducted between 16 and 50 m. However, precision in the measurements was better using images collected from 40 and 50 m altitudes (Figure 3).
Similarly, the difference between BHDF measurements of stationary dolphins by physical and UAS methods was 1 ± 2.4% ( Figure A3).
Across all altitudes, dolphin TL estimated through UAS photogrammetry using "surfacing" BHDF (i.e., TL Est.log.linear ; Equation S4) were overestimated by 3.3 ± 3.1% compared with their corresponding physical measurements ( Figure 4). All altitudes provided similar levels of accuracy, although greater precision was achieved for the three highest altitudes (Figure 4).

| Estimating TL using UAS measurements of BHDF
The ratio between physical measurements of BHDF and TL (Equation S1) was 29.2, with BHDF representing approximately 30% of TL. Applying this ratio (Equation S2), TL was underestimated by 0.2 ± 4.2% using physical measurements of BHDF. Using a linear relationship between TL and BHDF (p-value <.001, R 2 = .76, Figure A2), TL estimates based on physical measurements of BHDF were underestimated by 0.9 ± 3.2% and 1.0 ± 3.2% with the linear (Equation S3) and log-transformed linear models (Equation S4).
These results indicated that these models can be used to accurately estimate TL via BHDF (Table 2). Therefore, we used the same models to estimate TL of surfacing animals using UAS measurements of their BHDF. UAS-estimated TL were overestimated by 6.8 ± 3.8%, 3.4 ± 3.1%, and 3.3 ± 3.1% with the ratio, linear, and log-transformed linear models, respectively (Table 2).

F I G U R E 3 Mean differences (%)
in total length between physical measurements and UAS estimates of five stationary bottlenose dolphins. Errors are represented for each altitude (m, gray header) and individuals are colorcoded (a-e). The dashed line indicates zero difference. The horizontal bold line represents the median value, and the whiskers represent the upper and lower 25% of values. Sample sizes can be found in Table A2. UAS, Unoccupied Aerial System.

| Testing the performance of the age classifiers using UAS-simulated TL estimates
Mean age-classifier performance increased from 34.6% to 79.8% of correctly assigned individuals as the number of age-class bins was reduced (Table 3). Additionally, classifier performance was nearly equivalent between UAS-simulated BHDF measurements and TL estimates, with the BHDF method performing better for the youngest age-class bins (0-3 and 0-2 years, Table 3). Across all scenarios, performance was best in the youngest age-class bins. Overall, performance was best when using three age-class bins (around 72% for both TL and BHDF methods, Scenario D) or two age-class bins (79.8% and 79.1% for TL and BHDF methods respectively, Scenario E).
Finally, under Scenario B, we quantified where individuals were classified when not assigned to their correct age-class using UAS-simulated TL estimates ( Figure 5a) and UAS-simulated measurements of BHDF only (Figure 5b). Overall, 72.5%-93% of the individuals were correctly classified within two age-class bins (one age-class bin younger and older) of their actual age-class bin (Table 4a). Similar results were obtained when using UAS-simulated BHDF measurements only (Figure 5b; Table 4b).

| DISCUSS ION
Early detection of changes in vital rates of free-ranging delphinids due to environmental and anthropogenic stressors is needed to better forecast changes in population dynamics. Despite some caveats, we successfully tested and simulated a new approach using UAS photogrammetry to assess the population age structure of bottlenose dolphins, demonstrating the utility of UAS photogrammetry for quantifying age-class structure in free-ranging delphinid populations, which, in turn, can facilitate the detection of early signs of population changes.

Age-class bin scenario
Age

| Accounting for sources of error between physical measurements and UAS estimates
The precision and accuracy of UAS-estimated TL resulting from this study compare favorably with other photogrammetric methods used parameters of interest (i.e., TL, BHDF, age-class) was developed . Our frequentist approach addressed this uncertainty by smoothing the raw altitude data to account for laser reading uncertainty. However, this smoothing may underestimate the uncertainty in the measurements of TL (and slightly narrow down the error bars around these), and age classification. Future research should explore how the two different approaches to addressing uncertainty vary in age-class probabilities.
Despite these possible sources of errors, our findings support the accurate performance of UAS photogrammetry to infer TL based on BHDF measurements of surfacing animals.
Three modeling approaches were tested to estimate the TL of surfacing bottlenose dolphins from UAS-measured BHDF. Deriving TL using the TL/BHDF ratio provided the least accurate estimates. Results from the two other methods were similar, albeit with slightly better estimates using the log-transformed linear model. However, some limitations may arise from a log transformation, as it may make the data more variable and skewed (Feng et al., 2014

| Quantifying the age structure of the Sarasota dolphin community
Assigning individuals to age-classes via UAS photogrammetry using TL (via BHDF) or BHDF is a promising approach to inform population assessments when age-length growth curves are available for the study population. We obtained high classification scores when predicting the age of individuals to within two age-class bins of the actual ageclass ( Figure 5) and demonstrated that a narrower age-class bin width is less likely to correctly age-classify older animals (Table 3, Scenarios A and C) because of overlapping length distributions. Our findings highlight the importance of defining appropriate age-class bins for the study population. In this study, classifying individuals into three or two age-classes performed best. Our findings compared with those by Cheney et al. (2022), who correctly age-classified ~66% of the bottlenose dolphins they sampled (n = 54) in Scotland using five age-classes.
However, they concluded that TL determined via UAS photogrammetry was not fully reliable to correctly age-classify individuals.
In Sarasota, the age-length growth curve for the bottlenose dolphin reaches a plateau at 10-15 years (Read et al., 1993). Such a growth pattern may explain the difficulty in accurately estimating ages of individuals (via TL) for a range of ages that do not significantly differ in length (e.g., 10+ years old). Nonetheless, we demonstrated an acceptable age classification of younger dolphins (<10 years) independent of age-class bin width. In this study, the age classifier performance was better when fewer and broader age-class bins were used for assigning individuals based on UAS-simulated BHDF measurements and TL estimates, and was best when two age-classes were used ("0-10" and "10+" years, Table 3).
Similar accuracies were obtained whether using UAS-simulated BHDF measurements or associated TL estimates when ageclassifying individuals (Table 3). Since UAS-measured BHDF alone seems promising to quantify the age structure of free-ranging delphinid populations, there is potential for this method to be used for populations with little to no readily available demographic information. Although assumptions would have to be made about their age-length growth curves, large offshore populations may greatly benefit from this method since UAS photogrammetry could allow for efficient sampling of large groups.

| Age structure and conservation: applicability
Data-informed population models are required for the sustainable management of wildlife populations (Crouse et al., 1987;Morris et al., 2011). The age structure of individuals within a population is often at the center of these models, as other parameters such as individual growth (Clark et al., 2000) and survival and reproductive rates (Barlow & Boveng, 1991;Loison et al., 1999) vary by age. The ability to assign individuals to age-classes not only benefits the study of populations (Crouse et al., 1987;Holmes et al., 2007;Slooten & Lad, 1991), but it also enables the quantification of changes in TA B L E 4 Mean proportions of individuals correctly assigned within two age-class bins under Scenario B and simulated (a) UAS-estimated TL via BHDF measurements and (b) UAS-measured BHDF only. Note: Results were averaged over 1000 simulations. Shaded fused cells and bold numbers indicate the probability of assigning individuals to within two age-class bins of the actual age-class bin tested. Numbers in brackets represent the sample size per actual age-class bin.

Age-class Bins (years) Probability (%) of correct assignment in the following age-class bins
Abbreviations: BHDF, blowhole to dorsal fin distance; TL, total length; UAS, Unoccupied Aerial System.
survival and other parameters within and across age-classes (Holmes & York, 2003). For instance, survival through the first winter was strongly related to the length of bottlenose dolphin calves in Moray Firth, Scotland .
Unstable demographic structure (e.g., an unbalanced age structure or sex ratio) has significant implications for population dynamics (Jackson et al., 2020). In Moray Firth, an increase in juvenile/ adult bottlenose dolphin survival over a 25-year timespan was most likely caused by a 45% decrease in juvenile mortality rate (Civil et al., 2018). Booth et al. (2020) Norris et al., 1994;Östman-Lind et al., 2004, respectively). However, 9 years of similar surveys would be required to detect a 37% decline in this spinner dolphin stock (Tyne et al., 2016).
Designing surveys to determine the age structure of the groups encountered may facilitate understanding the overall age structure of the population studied. Faster detections of population changes may be facilitated using UAS photogrammetry as a practical and efficient tool to monitor the age structure of cetacean populations.

| CON CLUS ION
Our study demonstrates the use of UAS photogrammetry as a promising and reliable tool for monitoring the age structure of free-ranging delphinid species. Ultimately, UAS photogrammetry has the potential to more rapidly inform management compared with traditional survey methods. This technique, as one more tool combined with other more traditional approaches, can improve precision around population demographic estimates and therefore has the potential to improve the power of population monitoring (Jacobson et al., 2020).

CO N FLI C T O F I NTE R E S T S TATE M E NT
The authors declare no conflict of interest.

O PE N R E S E A RCH BA D G E S
This article has earned an Open Data badge for making publicly available the digitally-shareable data necessary to reproduce the reported results. The data is available at https://datadryad.org/stash/ dataset/doi:10.5061/dryad.d51c5b07p.

DATA AVA I L A B I L I T Y S TAT E M E N T
The data collected at Dolphin Quest used to conduct the analyses reported in this manuscript are available through the Dryad Digital Note: Shaded cells highlight individuals for which three measurements were not possible because either a flight was not conducted (-) or the flight resulted in fewer than three images of sufficient quality. Individual F was removed from the analyses for both UAS platforms, while individual A was removed from the analysis for the APH-22 only.

TA B L E A 3
Inter-observer difference (mean ± SE) in total length (%) between physical-and Unoccupied Aerial System (UAS)-measured TL for stationary animals and BHDF for surfacing animals.

TA B L E A 4
Results from a paired Wilcoxon test (p-values) evaluating the difference in measurement accuracy across observers and platforms (DJI Inspire-2 and APH-22) for stationary animals (TL) and surfacing animals (BHDF).

Measurement accuracy (p-values) between:
Observer 1  Note: V represents the measure of similarity between compared values and n represents the sample size. CV represents the coefficient of variation within observations (expressed in percentage).

F I G U R E A 1
Location of the A) natural notch created by the overlap of the fluke lobes and B) notch where the fluke lobes separate. The natural notch created by the overlapping fluke lobes was used for total length measurement.

F I G U R E A 3
Mean differences (%) in BHDF between physical measurements and UAS-measurements of five stationary bottlenose dolphins. Errors are represented for each altitude (m, grey header) and individuals are color-coded (A-E). The dashed line indicates zero difference, and error bars represent 95% confidence intervals. BHDF, blowhole to dorsal fin distance; UAS, Unoccupied Aerial System.

Methods A1: Estimating dolphin total length (TL) using blowhole dorsal fin distance (BHDF) proxy measurements
Three models were used to estimate TL from BHDF: To test the performance of these models using the physical measurements of BHDF (Table 1), the parameter BHDF UAS was replaced by BHDF Physical .

Ratio of BHDF/TL
The first model consisted of estimating an overall mean ratio between the mean physical BHDF and TL measurements (Ratio BHDF/TL ) for each dolphin (n = 18) as follows: Then, TL estimates (TL Est.ratio , cm) for individual dolphins (n = 5) based on UAS-measured BHDF (BHDF UAS ) for surfacing animals were then calculated per altitude as follows: (S1) Ratio BHDF∕TL = Physical BHDF Physical TL F I G U R E A 4 Distribution of the probabilities of age-class bin assignment by actual age-class bin (i.e., each subplot with a blue header). An age-classifier was used to estimate how bottlenose dolphins were classified when not assigned to their correct age-class under Scenario B using (a) UAS-simulated TL from BHDF, and (b) UAS-simulated BHDF measurements only. For each sub-plot, the blue boxplot represents the correct assignment of the age-class. Results were averaged over 1000 simulations. BHDF, blowhole to dorsal fin distance; TL, total length; UAS, Unoccupied Aerial System.

Linear
Coefficients from a linear model ('lme4' package, R Core Team 2022) testing the relationship between physical measurements of TL and BHDF were used to estimate TL from UAS-measurements of BHDF (cm) from surfacing animals and per altitude, as follows: where TL Est.linear is the TL estimated from the linear model, a is the slope, b is the y-intercept, and BHDF UAS is the UAS-measured BHDF for surfacing animals.

Log-transformed linear
The relationship between TL and BHDF was not fully isometric (i.e., linear relationship); the linear model underestimated TL for larger BHDF measurements and overestimated TL for smaller BHDF measurements. Therefore, the response and predictor variables were log-transformed prior to using a linear model ('lme4' package, R Core Team 2022). TL (m) was estimated per altitude from UAS-measurements of BHDF from surfacing animals as follows: where TL Est.log.linear is the TL estimated from the log-transformed linear model, a is the slope, b is the y-intercept, and BHDF UAS is the UASmeasured BHDF for surfacing animals.

Methods A2: Calculating the error (%) between physical and UAS measurements
The % error in total length (TL) and blowhole to dorsal fin (BHDF) between the physical measurements and the UAS-measurements was calculated per altitude for each dolphin as follows: where D L represents the % error in TL, M UAS is the mean UASmeasured TL or BHDF (cm), and M P is the mean physical TL or BHDF